Characters Of Highest Weight Modules Research Articles

Closed form fermionic expressions for the Macdonald index

We interpret aspects of the Schur indices, that were identified with characters of highest weight modules in Virasoro (p, p′) = (2, 2k + 3) minimal models for k = 1, 2, . . . , in terms of paths that first appeared in exact solutions in statistical mechanics. From that, we propose closed-form fermionic sum expressions, that is, q, t-series with manifestly non-negative coefficients, for two infinite-series of Macdonald indices of (A1, A2k ) Argyres- Douglas theories that correspond to t-refinements of Virasoro (p, p′) = (2, 2k + 3) minimal model characters, and two rank-2 Macdonald indices that correspond to t-refinements of {mathcal{W}}_3 non-unitary minimal model characters. Our proposals match with computations from 4d mathcal{N} = 2 gauge theories via the TQFT picture, based on the work of J Song [75].

Characters of Highest Weight Modules Over Affine Lie Algebras are Meromorphic Functions

We show that the characters of all highest weight modules over an affine Lie algebra with the highest weight away from the critical hyperplane are meromorphic functions in the positive half of Cartan subalgebra, their singularities being at most simple poles at zeros of real roots. We obtain some information about these singularities.